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Ahnassi is a Khajiit female who can be found in Pelagiad's Halfway Tavern. If you are male (of any race) and either interested in a relationship or just looking to perform any and all quests you can get your hands on, you can talk to her. Females will not have an option for these quests (sorry, girls). Ahnassi, as a Khajiit, is something of a humanoid cat, which lends itself to a number of lewd jokes, but I will opt for the higher ground and abstain, leaving you to your imagination.
Note: a warning to all journal quest purists: even once you have completed all of her available quests, you will still have a journal entry for "Ahnassi, a Special Friend." This is not a glitch or bug. I personally hate having uncleared journal entries and this permanent entry irks me to no end. Just thought I'd warn you.
Initiate the Romance
Talk to Ahnassi about her "smooth moves," "her profession," and then accept her gift of friendship. Unlike the Baldur's Gate 2 romances, you don't have to worry about giving wrong responses or blowing the relationship because you didn't act soon enough. It is basically good-to-go at any time, and you can always pick it up again later. However, if it isn't obvious, you can't attack her and expect the relationship to continue (duh!).
Your New Friend
You're on your way now. Talk to her about being her new friend, and she'll present you with the topics of sharing a gift and sharing a care. These will be your "quest trigger" topics, so to speak. Her first little tidbit is that Hrordis upstairs has the Belt of Sanguine Fleetness. You can kill Hrordis and take the belt if you want, or not. Ahnassi's just was telling you in case you wanted to know. And yes, some of her "quests" are like this just pieces of information she passes along to you as the relationship starts to heat up. Oh, and hey: be discreet about snuffing Hrordis. Some folks don't take kindly to murder. Go figure.
Kill Daren Adryn
Explore the "share a gift" and "share a care" topics to get a potion of feather and learn that Daren Adryn frightens Ahnassi. She is too timid to outright order his execution, but if you're any kind of boyfriend at all, you'll get the hint. Head over to Gnaar Mok and visit Nadene Rotheran's shack. There are three folks inside, Daren among them. You can talk and all that kinda crap, but you are just as well served by just killing them all. When you return, Ahnassi will clear any bounties on your head (just for good measure) as well as giving you 36 Lessons of Vivec, Sermon 30.
Loot the Redoran Treasury
This is another tip quest. Ahnassi will tell you that the key to the Redoran Treasury in Vivec is in Dralor Manor in the Redoran Plaza in Vivec. Inside the manor, you'll find the key to two chests in the treasury in the chest of drawers in the manor's upstairs bedroom. The chests that it opens are in the lowest floor of the treasury. You can rob the treasury blind if you can avoid getting caught. Or you can forego the deal altogether. Like I said, it's just a tip.
Cure a Skooma Addict
Ahnassi had/has another mate, a Khajiit named J'Dhannar. This cat got hooked on skooma, and is wandering around in the St. Olms Canalworks of Vivec. You need to pick up a copy of Confessions of a Skooma Addict (there's one for sale at both Jobasha's Rare Books in the Foreign Quarter of Vivec and at Codus Callonus' bookstore in Ald'ruhn). Bring this book to J'Dhannar to help him out for Ahnassi.
A Very Special Friend
You've just graduated to being a special friend. Ahnassi will give you a key to her house in Pelagiad, and once you leave the Tavern, Ahnassi will be hereafter located in her home. Her house is your house, so make yourself at home.
Talk to her about sharing a gift, and she'll throw you this slice of pie: Senyndie is the acrobatics secret trainer and a good friend of Ahnassi's. Feel free to stop in the Vivec Arena's Fighters' Quarters to get some training from Senyndie mention Ahnassi and she'll give you a discount as well as a copy of The Black Arrow, Volume I.
Give Her Flowers
In case you're the type of guy who needs to be told, Ahnassi likes flowers. She wants you to get two one is for her and one is for you, but you have to get both even if you're not exactly into flowers yourself. Fetch a gold kanet flower and a coda flower. The gold kanet is pretty common, but the coda flower isn't. However, if you don't mind the trip to Vivec, there is a bunch of them around the Shrine to Stop the Moon on the Temple Canton in Vivec. Otherwise, coda flowers are found in draggle-tail plants, but not all of them and an ampoule pod will NOT do.
Fetch Mavon Drenim's Flamemirror Robe
Actually, any Flamemirror Robe will suffice, but this is what she tells you to do. Mavon Drenim is in the Telvanni Tower off the Telvanni Plaza in Vivec. His robe is in the closet. I always kill the guy, but it's up to you. He will not take kindly to your theft, so he may force your hand. Bring the robe back to Ahnassi and she'll give you the option of keeping it yourself or giving it to her. If you give her the robe, she gives you 20 ebony darts.
Find Elvul's Black Blindfold
Ahnassi's last adventure requires you to go to Ebonheart's Imperial Commission. She wants you to retrieve a glove located therein and will disclose the location of a secret passage to get you there. Ignore her directions if you want the secret entrance does not save you any work or confrontation. Enter the Ebonheart Grand Council Chambers and from there, the Imperial Commission. Head downstairs and you'll see the two guards there. You want to enter the locked door nearest the bottom of the stairs (see, Ahnassi's secret passage leads to the room next to this one, so you'd still have to somehow pick this lock in the presence of these guards
the upside (?) to Ahnassi's route is that you may run into Furius Acilius, who is in the Ebonheart Underground Caves, and he's wearing the Lord's Mail; there is also a Glass Frostsword and a Glass Jinkblade hidden down there: the Frostsword is on a ledge above Furius and the Jinkblade is among some mushrooms in a dead-end passage to the east). Anyway, get inside this room (you can try to pickpocket Rufinus Alleius upstairs for the key, but you're no more likely to be successful at that than picking this lock in front of the guards, so pick (ha! get it?) your poison). Once within, you'll want to get inside the chest of drawers to get the glove. Bring it back to Ahnassi and she'll tell you to keep it. Isn't that kind of annoying?
A VERY Special Friend
Uh, that's it actually. You will not get anything else out of Ahnassi. You can rest in her house and use her stuff if you like. Kind of anti-climatic, ain't it?